A couple things:
- Traditional JFETs are made by diffusion. This is a thermally driven process, and the amount of dopant (concentration and spread) varies strongly with time and temperature.
- The channel is very thin (some µm), so it's very sensitive to the amount of diffusion. Cook it just a little too long and you have a pair of diodes instead of a JFET; not long enough and you have a resistor (or maybe a UJT). So, even an extremely finely tuned process can end up with its variations greatly magnified for a transistor like this.
- There are other processes possible, like, I see a few hits for epitaxial JFETs. It appears they can make them with a mixture of processes (epitaxy, diffusion, ion implantation), allowing more precise formation of the gate, and the channel within.
- If you confine your search to bad* old parts, of course you're going to see bad variances! Take the famous(ly old?) 2N3819 for example: -0.5 to -7.5V pinchoff, IDSS 2 to 20mA! Most families at least had the courtesy to divide them into three or so offerings. Contrast with, say, the classic (now obsolete) BF862, -0.3 to -1.2V pinchoff and 10-25mA IDSS. CPH3910 is more or less the modern replacement, offering -0.6 to -1.8V pinchoff and 20-40mA IDSS.
- Which compares alright with MOSFETs: a typical logic-level switching transistor might have 0.8 to 2V VGS(th) for example. Which is partly limited by diffusion (carrier density in the channel), and by gate oxide thickness (which also varies yfs for obvious(?) reasons).
*Just in the sense of this question, I mean. Also for sake of note, Jxxx series parts are all, I think, pretty old, contemporary with 2Nxxxx parts?
Disclaimer: I'm no transistor/IC expert; take this as a jumping-off point for further research. I would expect contemporary (1960s, 70s?) books on semiconductor design and manufacture, to hold many answers? These aren't particularly easy to search for online, but perhaps a physical library can help out.